PPT Slide
As demonstrated in text section 11.3 (p. 461, equation 11.18), in balanced three-phase systems, the total three-phase instantaneous power is constant.
This is analogous to the total power output of an automobile’s multi-cylinder ICE (i.e., what would happen if all cylinders fired at the same time?)
S3ph = 3Sph = 3Vph(Iph)* = 3|Vph||Iph|(cosq + jsinq) where q is the power factor angle (e.g., Z’s angle)
But 3|Vph||Iph| is the three-phase apparent power |S3ph| = Ö3|Vll||Il|
Ergo, S3ph = Ö3|Vll||Il|(cosq + jsinq) = P3ph +jQ3ph
\ P3ph = |S3ph|cosq = Ö3|Vll||Il|cosq and
Q3ph = |S3ph|sinq = Ö3|Vll||Il|sinq
Section 11.3: Power in Three-Phase Systems